Distribution Functionals

A collection of S4 classes that provide a flexible and structured way to work with probability distributions.

Usage

# S4 method for class 'Distribution,missing'
d(distr, x, ...)

# S4 method for class 'Distribution,missing'
p(distr, x, ...)

# S4 method for class 'Distribution,missing'
qn(distr, x, ...)

# S4 method for class 'Distribution,missing'
r(distr, n, ...)

# S4 method for class 'Distribution,missing'
ll(distr, x, ...)

# S4 method for class 'Distribution,missing'
mle(distr, x, ...)

# S4 method for class 'Distribution,missing'
me(distr, x, ...)

# S4 method for class 'Distribution,missing'
same(distr, x, ...)

Arguments

distr

a Distribution object.

x, n

missing. Agruments not supplied.

...

extra arguments.

Value

When supplied with one argument, the d(), p(), q(), r() ll() functions return the density, cumulative probability, quantile, random sample generator, and log-likelihood functions, respectively.

Details

When x or n are missing, the methods return a function that takes as input the missing argument, allowing the user to work with the function object itself. See examples.

See also

moments, loglikelihood, estimation, Bern, Beta, Binom, Cat, Cauchy, Chisq, Dir, Exp, Fisher, Gam, Geom, Laplace, Lnorm, Multigam, Multinom, Nbinom, Norm, Pois, Stud, Unif, Weib

Examples

# -----------------------------------------------------
# Beta Distribution Example
# -----------------------------------------------------

# Create the distribution
D <- Beta(3, 5)
x <- c(0.3, 0.8, 0.5)
n <- 5

# Density function
df <- d(D) ; df(x) # df is a function itself
#> [1] 2.268945 0.107520 1.640625
d(D, x) # alternative way to use the function
#> [1] 2.268945 0.107520 1.640625

# Distribution function
pf <- p(D) ; pf(x)
#> [1] 0.3529305 0.9953280 0.7734375
p(D, x)
#> [1] 0.3529305 0.9953280 0.7734375

# Inverse distribution function
qf <- qn(D) ; qf(x)
#> [1] 0.2763397 0.5167578 0.3641161
qn(D, x)
#> [1] 0.2763397 0.5167578 0.3641161

# Random Generator function
rf <- r(D) ; rf(n)
#> [1] 0.27315023 0.50569543 0.11579971 0.48033934 0.09075043
r(D, n)
#> [1] 0.2786339 0.3647822 0.4869432 0.2139102 0.4708356